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HSPT Math : Percentages

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Example Question #71 : Percentages

is 40% of 150.

is 30% of 200.

is 20% of 225.

Which are equal to each other/one another?

Possible Answers:

and

No two of , , and are equal.

and

Correct answer:

and

Explanation:

is 40% of 150, which is

$150 \times 0.40 = 60$

is 30% of 200, which is

$200 \times 0.30 = 60$

is 20% of 225, which is

$225 \times 0.20 = 45$

The correct response is Z < X = Y .

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Example Question #591 : Concepts

What is the percentage of male students in a class if are male out of students?

Possible Answers:

60%

$100\%$

$50\%$

$75\%$

Correct answer:

$75\%$

Explanation:

First you want to make a proportion so $\frac{15}{20}$ of the class are male.

You can reduce this fraction by since both the numerator and denominator are divisible by it.

This gives you $\frac{3}{4}$ which as a decimal is 0.75 .

To make that into a percentage, you multiple by 100 and add a "%" symbol.

So that gives you $75\%$ .

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Example Question #73 : Percentages

is 85% of .

What percent must be increased by to obtain ?

(Choose the closest answer)

Possible Answers:

$16 \%$

$18 \%$

$15 \%$

$17 \%$

Correct answer:

$18 \%$

Explanation:

The reasoning is independent of the value of , so assume that B = 100 .

is 85% of , so A = 85 .

To find out by what percent must be increased by to obtain , calculate

$\frac{B - A}{A} \cdot 100 \%$

This is

$\frac{100 - 85 }{85} \cdot 100 \%$

$\frac{1 5 }{85} \cdot 100 \%$

$\approx 17.6 \%$

The correct choice is 18%.

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Example Question #591 : Arithmetic

is one-third of , which is four-fifths of . What percent of is ?

Possible Answers:

$240 \%$

$26 \frac{2}{3} \%$

$375 \%$

$41 \frac{2}{3} \%$

Correct answer:

$375 \%$

Explanation:

is four-fifths of , so $B = \frac{4}{5}C$ .

is one-third of , so

$A = \frac{1}{3} B =\frac{1}{3} \cdot \frac{4}{5}C = \frac{4}{15}C$

$\frac{15} {4}\cdot A = \frac{15} {4}\cdot \frac{4}{15}C$

$\frac{15} {4} A = C$

is $\frac{15} {4}$ of ; the percent equivalent is that is

$\frac{15} {4} \times 100 \% = 375 \%$

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Example Question #75 : Percentages

is three-fourths of and three-fifths of . What percent of is ?

Possible Answers:

$80 \%$

$36 \%$

$125 \%$

$277 \frac{7}{9} \%$

Correct answer:

$80 \%$

Explanation:

For simplicity's sake, we will set B = 100 ; this reasoning is independent of the value of .

is three-fourths of - that is,

$A = \frac{3}{4} B = \frac{3}{4} \cdot 100 = 75$ .

Since is also three-fifths of ,

$A = \frac{3}{5} C$

$75 = \frac{3}{5} C$

$\frac{5} {3}\cdot 75 = \frac{5} {3}\cdot \frac{3}{5} C$

125 = C

To find what percent is of , calculate:

$\frac{B}{C} \cdot 100 \% = \frac{100}{125} \cdot 100 \% = 80 \%$

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Example Question #71 : Percentages

What is $\frac{1}{3}$ % of 60?

Possible Answers:

18,000

$1 \frac{4}{5}$

2,000

$\frac{1}{5}$

Correct answer:

$\frac{1}{5}$

Explanation:

$\frac{1}{3}$ % of 60 can be calculated as follows:

$\frac{\frac{1}{3}}{100} \cdot 60 = \frac{1}{3} \cdot \frac{1}{100} \cdot \frac{60 }{1}= \frac{60}{300}= \frac{1}{5}$

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Example Question #71 : Percentages

$\frac{2}{3}$ is what percent of $\frac{5}{7}$ ?

Round to the nearest whole percent.

Possible Answers:

$47 \%$

$210 \%$

$107 \%$

$93 \%$

Correct answer:

$93 \%$

Explanation:

To calculate what percent $\frac{2}{3}$ is of $\frac{5}{7}$ , evaluate:

$\frac{\frac{2}{3}}{\frac{5}{7}} \times 100$

$= \frac{2}{3} \div \frac{5}{7} \times \frac{100}{1}$

$= \frac{2}{3} \times \frac{7} {5}\times \frac{100}{1}$

$=\frac{1400}{15}$

$\approx 93$

The closest answer is 93%.

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Example Question #72 : Percentages

30% of is equal to 40% of what number?

Possible Answers:

12 N

$\frac{1}{12}N$

$\frac{4}{3}N$

$\frac{3}{4}N$

Correct answer:

$\frac{3}{4}N$

Explanation:

30% of is equal to $\frac{30}{100} N = \frac{3}{10}N$ . Divide by 40%, or $\frac{40}{100} = \frac{4}{10}$ , to get

$\frac{3}{10}N \div \frac{4}{10} = \frac{3}{10}N \cdot \frac{10} {4} = \frac{3}{4}N$

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Example Question #73 : Percentages

percent of 1,000 is equal to what percent of 5,000?

Possible Answers:

$\frac{1}{20}N$

20N

$\frac{1}{5}N$

Correct answer:

$\frac{1}{5}N$

Explanation:

percent of 1,000 is equal to

$\frac{N}{100} \cdot 1,000 = 10 N$

This is

$\frac{10N}{5,000} \cdot 100 = \frac{1,000N}{5,000} = \frac{1}{5}N$

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Example Question #601 : Arithmetic

0.5 is what percent of 0.001 ?

Possible Answers:

$5 00 \%$

$50,000 \%$

$0.2 \%$

$0.002 \%$

Correct answer:

$50,000 \%$

Explanation:

To find what percent 0.5 is of 0.001, evaluate:

$\frac{0.5}{0.001} \times 100 \%$

$= \frac{0.5 \times 100}{0.001} \%$

$= \frac{50}{0.001} \%$

$= 50,000 \%$

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HSPT Math : Percentages

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #71 : Percentages

Example Question #591 : Concepts

Example Question #73 : Percentages

Example Question #591 : Arithmetic

Example Question #75 : Percentages

Example Question #71 : Percentages

Example Question #71 : Percentages

Example Question #72 : Percentages

Example Question #73 : Percentages

Example Question #601 : Arithmetic

All HSPT Math Resources

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